Unitary evolution Definition and 17 Threads

The usual justification for why the evolution of physical systems is unitary in quantum mechanics involves arguments like "probabilities must sum to 1" or similar arguments that apply equally to any CPTP map. I'm just curious what justifications people here would use for selecting out unitary...

Now from the relevant equations, $$U(t) = \exp(-i \omega \sigma_1 t)$$ which is easy to compute provided the Hamiltonian is diagonalized. Writing ##\sigma_1## in its eigenbasis, we get $$\sigma_1 = \begin{pmatrix} 1 & 0\\ 0 & -1\\ \end{pmatrix} $$ and hence the unitary ##U(t)## becomes...

In QM, states evolve in time by action of the Time Evolution Unitary Operator, U(t,t0). Without the action of this operator, states do not move forward in time. Yet even stationary states, like an eigenstate of energy, still contain a time variable – they oscillate in time at a fixed...

Because I understand that for unitary evolution, MWI is required, which suggests that for different interpretations, there may not be unitary evolution?

In his book "the black hole war" Susskind writes that in quantum mechanics information cannot be lost because it is unitary. As collapse is not unitary does he say that collapse never occurs?

If we consider the Unitary evolution of the wavefunction, and interpret measurements as becoming in superposition, taking it that the measurement device gets in a superposition of spin up and spin down, do two measurement devices that each measure one particle of an entangled pair become...

What do we mean when we say that a system can't change (in time) because its evolution is unitary?

<< Mentor Note -- thread moved from Homework Help forums to General Math >>[/color] Good day, I run coding in Mathematica. But, I get singular matrix A at certain loop. In theory, how can I make matrix A become orthogonal A=\begin{pmatrix} 0& 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0& 0 & 0 & 0 & 0 &...

Imagine potential well which in t=0 switches to a different potential well (instantly), like in the picture below. So in negative times the wavefunction density should tend to be localized in the first well, in positive times to be localized in the second well...

[This thread split from https://www.physicsforums.com/threads/is-collapse-indispensable.854384/] I don't know a reference but I can indicate a proof. Ergodicity of unitary evolution of the wave function says that for given ##\psi_0## of norm 1, ##\psi(t)=e^{-itH}\psi_0## comes for some ##t##...

I have question about unitary evolution. As I understand it is assumed that unitary evolution concerns only quantum system and there are no changes in environment. First, I would like to ask if my understanding is correct? Second, from where comes this assumption? Does it comes with Schrodinger...

I am aware that physicists are trying to derive born rule from unitary evolution. Has there been any success? What is the current status of that program?

I think this is the right forum for this.. are there any physical reasons to assume the evolution of a quantum system is given by a group of unitaries rather than a semigroup of isometries (or, if you're in the Heisenberg picture, group of automorphisms rather than semigroup of endomorphisms)...

A philosophy that underpins many approaches to understanding quantum mechanics (the many worlds interpretation in particular, but collapse models and other related ideas also) is that continuous Schroedinger evolution is somehow `nicer', `preferred', or `more fundamental' than the "damned...

If we treat space and time equally, in classical QM, by defining, formally, a time observable (and a conjugate observable), we can see that the postulates of QM have a simpler form: we can derive the unitary evolution from the measurment collapse postule. (We use the units hbar=1). Just take...

This is for those who believe QM includes a phase of unitary evolution. In ordinary QM the state is given by a complex vector (actually a ray) in Hilbert space and it evolves by unitary operators transforming it. Does this complex thing and its behavior exist in out spacetime? If not, then...

This thread is based on some reading I've done on decoherence (a lot of it by Zurek) and recent experiments involving decoherence and complementarity. One interesting item is the recent experiment by Anton Zeilinger and team involving C60 molecules interacting to produce and interference pattern...